Rigorous derivation of the Landau equation in the weak coupling limit

We examine a family of microscopic models of plasmas, with a parameter $\alpha$ comparing the typical distance between collisions to the strength of the grazing collisions. These microscopic models converge in distribution, in the weak coupling limit, to a velocity diffusion described by the linear Landau equation (also known as the Fokker-Planck equation). The present work extends and unifies previous results that handled the extremes of the parameter $\alpha$, for the whole range (0, 1/2], by showing that clusters of overlapping obstacles are negligible in the limit. Additionally, we study the diffusion coefficient of the Landau equation and show it to be independent of the parameter.Comment: 22 pages, 8 figures, accepted to Communications in Pure and Applied Analysi

Outstanding Issues in Our Understanding of L, T, and Y Dwarfs

Since the discovery of the first L dwarf 19 years ago and the discovery of the first T dwarf 7 years after that, we have amassed a large list of these objects, now numbering almost six hundred. Despite making headway in understanding the physical chemistry of their atmospheres, some important issues remain unexplained. Three of these are the subject of this paper: (1) What is the role of "second parameters" such as gravity and metallicity in shaping the emergent spectra of L and T dwarfs? Can we establish a robust classification scheme so that objects with unusual values of log(g) or [M/H], unusual dust content, or unresolved binarity are easily recognized? (2) Which physical processes drive the unusual behavior at the L/T transition? Which observations can be obtained to better confine the problem? (3) What will objects cooler than T8 look like? How will we know a Y dwarf when we first observe one?Comment: 11 pages including 5 figures. To appear in the conference proceedings for Cool Stars 1

New spectral types L and T

The establishment of new spectral classes cooler than type M has had a brief, yet already rich, history. Prototypes of the new "L dwarf" and "T dwarf" classes were first found in the late 1980s to mid-1990s, with a flood of new discoveries occurring in the late 1990s with the advent of deep, large-area, digital sky surveys. Over four hundred and fifty L and T dwarfs are now cataloged. This review concentrates on the spectroscopic properties of these objects, beginning with the establishment of classification schemes rooted in the MK Process. The resulting grid of spectral types is then used as a tool to ferret out the underlying physics. The temperature ranges covered by these spectral types, the complex chemical processes responsible for the shape of their emergent spectra, their nature as either true stars or brown dwarfs, and their number density in the Galaxy are discussed. Two promising avenues for future research are also explored: the extension of the classification system to three dimensions to account for gravity- and metallicity-dependent features, and the capability of newer large-area surveys to uncover brown dwarfs cooler than those now recognized

Probabilistic methods for discrete nonlinear Schr\"odinger equations

We show that the thermodynamics of the focusing cubic discrete nonlinear Schrodinger equation are exactly solvable in dimensions three and higher. A number of explicit formulas are derived.Comment: 30 pages, 2 figures. To appear in Comm. Pure Appl. Mat

Financial Development, Economic Growth, and Poverty Reduction

The frequent failure of financial liberalisation efforts in developing countries, and the serious damage which recent financial crises have imposed on these economies, have led to renewed attempts to understand the relationships between financial sector development, economic growth and poverty reduction, and to provide a more robust intellectual foundation on which to design efficient and pro-poor financial sector policies for developing countries. The paper examines the contribution that financial sector development can make to poverty reduction in developing countries. The linkages between financial and economic growth, and between economic growth and poverty reduction, are considered, and some preliminary empirical evidence is presented on these linkages. The paper goes on to argue that financial market imperfections are a key constraint on pro-poor growth, and that public policy directed at the correction of these financial market failures is needed to ensure that financial development contributes effectively to growth and poverty reduction. The final part of the paper examines in some detail the role of financial regulation and supervision policy as a key area for public intervention directed at enhancing the financial sector’s contribution to poverty reduction.